Excitation spectrum of a magnetic domain wall containing Bloch lines

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Abstract
The excitation spectrum of a ferromagnetic domain structure consisting of an infinite planar Bloch wall containing Bloch lines is examined. The material is considered to have pure uniaxial anisotropy, and demagnetizing effects are ignored. In this case an exact solution for the static configuration is available and the Schrödinger equation for the excitations is separable. The separated equation is solved exactly in closed form and the solutions normalized. The solutions are of three types: localized to the wall, totally reflecting, and partially transmitting. The Bloch lines introduce a cutoff into the dispersion relation for the waves localized to the wall somewhat in the manner of a lumped delay line. Spin waves impinging on the wall are diffracted by the Bloch lines. The stress tensor formalism for this system is developed and applied to computing the radiation pressure of the spin waves. A discussion of the application of domain-wall modes to the interpretation of various experimental results, both static and dynamic, is given. The mode picture offers an alternative interpretation of the experimental results in some cases and the only interpretation in others.